Some of the commentary on the internet has been not especially well informed, for example there are some crazy claims at https://news.ycombinator.com/item?id=3668310. If you're in a "someone is wrong on the internet!" correcting mood, you might want to go leave some comments in furtherance of the collective intelligence of mankind.

ENOB stands for Effective Number of Bits and is another measure of a DAC’s performance. No 24 (or 32) bit audio DAC can achieve true 24 bit performance, In fact, 20 ENOB is generally considered the “Holy Grail” of real world DAC performance. The ODAC is just under 19 ENOB and the Benchmark [DAC1], even referenced to its full 7+ volt maximum output, is 19.3 ENOB. The FiiO E10, even in 24 bit mode, is only 16.2 ENOB.

Note: the guy is touting his own design for a DAC/headphone amp combo (referenced above as ODAC), but he has a good track record of providing what looks like precise measurements, and making sense…

The answer depends on conditions, like the chem lab experiments. At standard temperature and pressure ... .20 bits is pushing the limit for practical purposes, thermal noise is too high for anything better. For some endeavors, such as some aspects of radio astronomy, cutting edge particle physics, and military systems, cryogenic cooling is practical and common place. Liquid nitrogen, or even more extreme materials, with the low temperatures they provide, considerably reduce the intrinsic device noise levels.

So ... at least it is not the case that a DAC fed a 192/24 signal as oppsed to a 48/20 or 44.1/16, will have to operate at higher load --> more thermal noise --> lower e.n.o.b.? (Shouldn't be, it is not that demanding?)

At the risk of spinning off a digression: what is the maximum effective number of bits available in a DAC these days -- and does that number depend on the sampling frequency?

Effective number - you mean in terms of resolution that is actually delivered to the analog domain?

Check the TI and ESS web sites. They seem to be flogging the SOTA in this regard the hardest.

I think that noise down 133 dB down is the SOTA - what about 21 bits? If you want to be hard to please you would also demand that spurious responses (IM+THD) would also be part of the equation, in which case things seem to be about 3-6 dB worse.

I basically agree with the 20 bit number that others have put forth.

There is a strategy for improving the dynamic range of a DAC that can be expanded almost endlessly, at a increasingly high cost. Run multiple DACs that each generate statistically independent noise in parallel. Dynamic range improves by 3 dB for every doubling of DACs. I believe that ESS goes to 4x or even 8x for specing their products.

The progression is:

2 DACs in parallel, get a 3 dB improvement4 DACs in parallel, get a 6 dB improvement8 DACs in parallel, get a 9 dB improvement16 DACs in parallel, get a 12 dB improvement...

Thing is, this does nothing for spurious responses because they are always coherent, like the signal. The ratio between spurious responses and signal remains the same as you add DACs.

In the past people have run DACs in antiphase which can help even-order distortion. But you only get one iteration of that approach.

As DAC functionality gets cheaper and cheaper, the numbers race may cause these approaches to be more common. But, a good single DAC is overkill enough!

After measuring about a hundred audio interfaces, the overwhelming majority being Sigma-Delta, it seems to be a general rule that the best effective performance is found at lower sample rates (e.g. 44 KHz), all other things being equal.

Some of the commentary on the internet has been not especially well informed, for example there are some crazy claims at https://news.ycombinator.com/item?id=3668310. If you're in a "someone is wrong on the internet!" correcting mood, you might want to go leave some comments in furtherance of the collective intelligence of mankind.

One more page to link to if asked for some explanation, many thanks for that. What saddens me is the resulting discussion on this news channel.There the typical "I am enigineer" come in and simply claim that "Nyquist was wrong because i can hear all these harmonics!"

So ... at least it is not the case that a DAC fed a 192/24 signal as oppsed to a 48/20 or 44.1/16, will have to operate at higher load --> more thermal noise --> lower e.n.o.b.? (Shouldn't be, it is not that demanding?)

Usually they operate at about the same internal clock speed regardless of sampling rate, just with different oversampling ratios. Wouldn't make sense to run a DAC made for high speed operation at a lower speed, since more oversampling means less risk of aliasing and generally less quantization noise.

Also, in this context, thermal noise doesn't necessarily refer to the temperature of the A/D alone, but also to the temperature of everything its hooked up to. The terminating resistance in whatever the A/D is reading still contributes the same thermal noise no matter how cool you make the A/D for instance. This is why refrigeration is not a great option like it is in optical detectors.

Audibility of a CD-Standard A/D/A Loop Inserted into High-Resolution Audio Playback [...]Not one listener throughout the entire test was able to identify which was 16/44.1 and which was high rate, and the 16-bit signal wasn't even dithered!

Not to be nitpicky, but IMHO you only dither if you resample digitally?

I'm happy to see a truly coherent argument against the necessity for higher bit depths and sample rates.

Waste of storage space is a small margin of disadvantage however. The advocates of 24/96 and higher were happy to pay the cost of increased storage space to achieve a perceived advantage, and storage space (or transmission bandwidth) is an increasingly cheap commodity.

This leaves us with degradation of fidelity as a result of processing unnecessary ultrasonics. Unfortunately the very same tests (Meyer and Moran) we used to make our case previously now mitigate against us. If a 16/44k1 bottleneck is inaudible in a system avowedly processing ultrasonics, then the ultrasonics cannot reasonably be said to have (audibly) degraded the sound.